Question

If $y$ is directly proportional to $x$ and if $y=20$ when $x=6$, what is the value of $y$ when $x=9$?

• A. $\frac{10}{3}$
• B. $\frac{40}{3}$
• C. $23$
• D. $27$
• E. $30$

Answer 1

The correct option is E $30$

Given that: ${}^{\prime }{y}^{\prime }$ is directly proportional to ${}^{\prime }{x}^{\prime }$,

Formally, it is expressed as

$y$ $=$ $k$$x$ where, ${}^{\prime }{k}^{\prime }$ is a constant

To find the value of ${}^{\prime }{k}^{\prime }$,

As $y$ $=$ $20$ when $x$ $=$ $6$,

$\Rightarrow y$ $=$ $k$$x$

$\Rightarrow y$ $=$ $k$ $\times$ $x$

$\Rightarrow 20$ $=$ $k$ $\times$ $6$

$\Rightarrow k$ $=$ $\frac{20}{6}$

$\Rightarrow k$ $=$ $\frac{10}{3}$

Now, $y$ $=$ $\frac{10}{3}$$x$

To find ${}^{\prime }{y}^{\prime }$ when $x$ $=$ $9$,

$\Rightarrow y$ $=$ $\frac{10}{3}$$x$

$\Rightarrow y$ $=$ $\frac{10}{3}$ $\times$ $x$

$\Rightarrow y$ $=$ $\frac{10}{3}$ $\times$ $9$

$\Rightarrow y$ $=$ $30$

Therefore, the value of ${}^{\prime }{y}^{\prime }$ when $x$ $=$ $9$ is ${}^{\prime }{30}^{\prime }$.